Numerical analysis of convective-radiative heat transfer in an air enclosure with a local heat source

Mathematical simulation of natural convection and surface radiation in a square air enclosure having isothermal vertical walls with a local heat source of constant temperature has been carried out. Mathematical model has been formulated on the basis of the dimensionless variables such as stream function, vorticity and temperature by using the Boussinesq approximation and diathermancy of air. Distributions of streamlines and isotherms reflecting an effect of Rayleigh number $10^3\leq{Ra}\leq10^6$, surface emissivity $0\leq\varepsilon\leq1$, ratio between the length of heat source and the size of enclosure $0.2\leq{l/L}\leq0.6$ and dimensionless time $0\leq\tau\leq100$ on fluid flow and heat transfer have been obtained. Correlations for the average heat transfer coefficient in dependence on $Ra, \varepsilon$ and $l/L$ have been ascertained.